According to Hobbes chaos or a "state of nature" is present when "there is a lack of authority and there exists a perpetual state of war". In the Hunger Games movie, it could be argued both ways that a state of nature exists.Hobbes even says "To this war of every man against every man this also is consequent, that nothing can be unjust". There are many factors that can support each claim so in my opinion, I don't think there is a right or wrong viewpoint.
To start, the Hunger Games show this idea when all the tributes enter the arena. In it there are no laws, and no justice system. Each person is free to do whatever it takes to stay alive and win the Games, including killing others. Hobbes stated, "Where there is no common power, there is no law; where no law, no injustice". This applies directly to the Games because there is no central power, rather everyone is on their own trying to stay alive. Therefore, nobody is breaking any laws if there are none to begin with. Also, Hobbes talks about a state of war, which is pretty self explanatory, that is evident in the movie. The best example is at the beginning when half of the tributes are killed near the Cornucopia. The scene is similar to a war battle because people are being brutally murdered and bodies lying all over the ground.
On the opposite side of the argument, the Games are controlled by the Capitol and are designed to kill the tributes. In fact, there is a person in charge of monitoring the entire Games called the Gamesmaker, and Seneca Crane had this job. They had this huge screen that showed where every tribute was and what they were doing at that time. They could also create scenarios to influence the decisions of the tributes. For instance, they created a large fire to move Katniss towards the other group. This aspect isn't a state of nature because the Capitol is controlling what happens inside the arena. Additionally, before the Games actually begin, each of the tributes get treated like they are celebrities and are given luxurious things. Katniss and Peeta are brought to the Capitol on a train with what looks like a buffet of food, and once they get there they stay in a penthouse suite. Quite the opposite treatment of what one would originally think before fighting it out to the death. The Capitol just wants to put on a good show as well as send a message to each of the districts.